1. Modelling SEDs with Artificial Neural Networks Laura Silva (INAF/Trieste) GianLuigi Granato (INAF/Trieste), Andrew Schurer (INAF/Padova), Cesario Almeida, Carlton Baugh, Cedric Lacey, Carlos Frenk (ICC/Durham) Outline: SED modelling- approaches vs aims GRASIL and application to SAM Modelling SED with ANN

2. Multi- SED modelling – approaches vs aims *Stellar pop. synthesis *SFR(t)+Mgas(t),Z(t) exponentials, chemical evol. or galaxy formation models * UV/optical attenuation and IR emission Semi-empirical: attenuation curve for L IR + IR shape Pros: non time consuming –analysis of large data sets. Cons: not great predictive power Theoretical: Explicit computation of radiative transfer and dust emission Pros: broader interpretative/predictive power Cons: time consuming

3. Modelling UV to radio SEDs with GRA(phite)SIL(icate) Star- forming MCs Diffuse dust Extincted stars 1) Realistic and flexible SED modelling Stars and dust in a bulge (King profile) + disk (double exponential) Dust: big grains, very small grains and PAHs. Emission is appropriately computed for each component Stars are born within MCs and gradually escape as a function of their age  age-dependent extinction 3 dusty environments: dense (star forming Molecular Clouds), diffuse (cirrus) (  clumping of stars and dust), dusty envelopes of AGB stars UV-to radio SEDs (continuum & nebular lines) 2) Reasonable computing time Radiative transfer exactly solved for opt thick MCs, with approximation in the cirrus (real bottle-neck) Presence of symmetries No Monte Carlo

4. Computing SEDs in Semi-Analytical galaxy formation Models SAM: DM with gravity-only N-body or MC, baryons with analytical recipes – compare with widest range of observed galaxy properties Outputs: simulated catalogues of galaxies at different redshift slices; SFR(t), Mgas(t), Z(t), morphology, scale radii for stars & dust Associate to each mock galaxy its “real” SED but: complexities in treating radiative effects - unknown dust properties - computing time fundamental issue for cosmological volumes  Semi-empirical treatment: fix  v (  L or  f(Mgas, Z)) + dependence + uniform distrib. of stars and dust in a 1D slab SAMs with theoretical SED: GALFORM+GRASIL (Granato+00, Silva+01, Baugh+05, Lacey+08) MORGANA+GRASIL (Monaco+07, Fontanot+07, 08) Anti-hierar.BarionicCollapse+GRASIL(Granato+04, Silva+05,Lapi+06)

5. SAM + GRASIL SAM + [C&F00 + slab] SF histories from the Semi-Analytical Model for galaxy formation MORGANA SED by: *GRASIL (colored) *Empirical [attenuation curve with C&F + slab] (hatched) Fontanot, Somerville, Silva+08 Different treatments predict different SED for the same SFR(t)

6. SAM + GRASIL SAM + [ C&F00 + slab ] SF histories from the Semi-Analytical Model for galaxy formation MORGANA SED by: *GRASIL (colored) *Empirical [attenuation curve with C&F + slab] (hatched) Net attenuation A(90°)-A(0°) vs M star

7. Fontanot, Somerville, Silva+08 SAM+GRASIL SAM+ templates [Chary&Elbaz01, Lagache+04, Devriendt+99] SF histories from SAM MORGANA SED by: *GRASIL (black) *Templates (color) Different treatments predict different SED for the same SFR(t)

8. GALFORM + GRASIL (Granato+00, Silva+01, Baugh+05, Lacey+08) But high-z universe : Revised model: reproduce multi- LFs and counts/ z-distr with top-heavy IMF in starbursts 850  m Old model 850  m New model Local universe : 0.2  m B-band K-band 60  m

9. Spectral variance for a GALFORM + GRASIL catalogue =>ANN: Mathematical algorithms for data analysis, introduced to replicate the brain behavior - learn from examples SEDs : complex, non-linear, high dimensionality and large variance functions of some galaxy properties ANN is a black box that is trained to predict the SED from controlling parameters using a suitable precomputed training set (many couples input-output) Improving the computing time: Modelling SEDs with Artificial Neural Neworks

10. Input layer: parameters determining the SED Output layer: SED, one unit for each L( ) Hidden layers: black box! w jk n j =  w jk i k o j =f(n j ) Propagation rule: the output from each unit is weighted and summed to form the input for the upper layer units: n j =  w jk i k The new output is o j =f(n j ), f=non linear function Learning: the ANN is trained with a given target- weights are adjusted to best approximate a given set of inputs/outputs

11. ANN & SED: 2 methods “Universal” and very fast (Silva+08): input = physical quantities determining the SED of MCs and Cirrus – one single trained net MCs: Optical depth, R/Rsubl. Cirrus: Ldust, Mdust, Polar & Equatorial opt depth, R*/Rdust, z*/R*, zdust/Rdust, Hardness of the rad. field “ANN mode” implemented in GRASIL: compute extinction and predict IR SEDs with separately trained ANN for MCs and Cirrus - ~ 1 sec. -> large cosmological volumes “Less universal” and super-fast (Almeida+08): input = galaxy properties – re-train the net for different realizations Mstar, Zstar, Zgas, Lbol, vcirc, R 1/2 (bulge & disc),  V, Mburst,  t last burst … Each simulated catalogue from a SAM requires a trained net exploit the whole Millennium Simulation

12. Examples: single objects M82 ARP220

13. m12.00zv2.50 @ 0.25 Gyrm13.00zv3.50 @ 0.25 Gry m13.20zv3.50 @ 0.1 Gyrm13.20zv3.50 @ 0.5 Gyr FULL/ANN Tot: black/red MC: dark /light green Cirr: blue/cyan Examples: models extracted from ABC SAM (G04, S05)

14. Examples: models extracted from a GALFORM+GRASIL catalogue Almeida et al.

15. …and one catastrophe ….work in progress….. m12.00zv2.50 @ 0.1 Gyr Improving the reconstructed SED by splitting the output neurons

16. GALFORM+GRASIL catalogue: >70% with error < 10% - MIR and submm have larger variance B-band 24  m 850  m 100(1-L predicted /L original ) vs L original Almeida et al.

17. Colours for z=0 GALFORM+GRASIL catalogue Almeida et al.

18. ABC SAM – Galaxy counts FULL: red ANN: blue 24  m 850  m

19. 24  m z=0.5 0.17  m z=3 850  m z=2 GALFORM+GRASIL: Luminosity Functions ______ original - - - - - - recontructed Almeida et al.

20. Summary Multi-wavelength modelling as a tool to quantitatively deconvolve/ interpret observations – make predictions/ constrain galaxy formation models Different treatments predict different SEDs for the same SFR(t)-> necessity of a reliable computation of the SED for proper interpretations of observations and predictions of galaxy formation models The treatment of dust reprocessing of UV/optical in the IR requires a proper computation – time cosuming for some applications For large cosmological applications: promising solution with ANN